Dynamics in a neigborhood of separatrices of an area-preserving map
We discuss the global structure of the separatrix branches in a two-dimensional area-preserving map and present some formulas estimating the width of stochastic layers, provided the map is near-integrable. The concept of the separatrix map is also discussed.
KeywordsInvariant Curve Separatrix Branch Homoclinic Point Stochastic Layer Hyperbolic Periodic Point
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- Lazutkin V. F. (1984): Splitting of separatrices for standard Chirikov's mapping, VINITI no. 6372-84, 24 Sept. (in Russian)Google Scholar
- MacKay R. S. (1983): A renormalization approach to invariant circles in area-preserving maps Physica 7D, p. 283–300Google Scholar
- Mather J. N., Invariant subsets for area-preserving homeomorphisms of surfaces, Mathematical Analysis and Applications, Part B. Advances in Mathematics. Supplementary Studies, Vol. 7B, Leopoldo Nachbin, ed.Google Scholar
- Olvera A. and Simó C. (1987): An obstruction method for the destruction of invariant curves Physica 26D, p. 181–192Google Scholar
- Poincaré H., Les méthodes nouvelles de la mécanique celeste, V. 1–3: Gauthier-Villars, Paris, 1892, 1893, 1899.Google Scholar
- Treschev D. (1998) Width of stochastic layers in near-integrable two-dimensional symplectic maps. to appear in Phys. D.Google Scholar
- Treschev D., Closures of asymptotic curves in two-dimensional symplectic maps. Preprint.Google Scholar
- Zaslavsky G. M. and Filonenko N. N. (1968): Stochastic instability of trapped particles and the conditions of applicability of the quasilinear approximation, Zh. Eksp. Teor. Fiz., v. 54, p. 1590–1602. (in Russian)Google Scholar